GEWU Magazine

Alternative Way of Solving the Ice-Type Models6 questions

Integrable manifolds and commuting transfer matrices of the odd eight-vertex model
Open for about 8 years
Extending the FPRAS for the six-vertex model with an unwindable constraint function beyond two-by-two-intersection-free circuit decompositions and the $b\le 1/\delta$ regime
Open for about 4 years
Deriving Bethe equations for the XYZ spin chain from the matrix-product-operator construction
Open for less than 1 year
Analytic proof of the even-index Yang–Baxter conjectures for descendants of the six-vertex model from the Drinfeld doubles of dihedral group algebras
Open for about 16 years
Completing the approximation-complexity classification of the six-vertex model: the white region of the disordered phase and the Tutte point $T(G;3,3)$ on planar graphs
Open for about 8 years
Completeness of the homogeneous $T$ – $Q$ Bethe ansatz for the eight-vertex model with quasi-periodic boundary conditions on an odd number of sites
Open for about 11 years

analytic Bethe Ansatz2 questions

Andrews–Baxter–Forrester model3 questions

ASEP/TASEP2 questions

Ashkin–Teller model3 questions

Ashkin–Teller self-dual line1 questions

Conformal-field-theory status of transverse-polarized (new) boundary conditions in quantum Potts chains and the transverse-polarized-blob duality beyond the solved endpoints

ballistic transport2 questions

basic hypergeometric functions1 questions

Multi-sum-to-single-sum transformations: other base summations, an underlying WP-Bailey chain, and combinatorial proofs of the embedded Jacobi-type identities (Mc Laughlin 2016)

Baxter

Q

operator4 questions

Bazhanov–Baxter three-dimensional lattice model2 questions

Bethe wave function3 questions

Bethe equations3 questions

Completeness of Bethe equations3 questions

Bethe lattice magnetization, free energy, and critical behavior2 questions

Bethe lattice recursion relations2 questions

Bethe lattice and Cayley tree3 questions

Bethe root density and hole density3 questions

Bethe roots and complex root structure1 questions

Analytic origin and finite-size scaling of the root-organisation rules in the open XXX spin-1/2 chain with non-diagonal boundary fields
Open for less than 1 year

Bethe state norm4 questions

Bethe Ansatz for stochastic processes3 questions

Bethe strings and string hypothesis2 questions

Bond-dimension extrapolation2 questions

bootstrap principle2 questions

Bosonic/fermionic character representation3 questions

boundary

S

matrix3 questions

boundary crossing-unitarity4 questions

boundary entropy1 questions

Tracy-Widom TBA for exact g-functions beyond the self-dual sinh-Gordon point: bound states, internal degrees of freedom, excited states, and the SoV normalization

boundary Yang–Baxter equation3 questions

Braid group representation1 questions

Faithfulness of the Bardakov-Bellingeri conjugation representations of surface braid groups on free groups

CDD factor3 questions

corner environment3 questions

corner environment contraction3 questions

Corner Transfer Matrices7 questions

Coulomb-gas representation4 questions

Origin and mechanism of CP violation and its cosmological connection7 questions

CTM eigenvalues3 questions

Integrable manifolds and commuting transfer matrices of the odd eight-vertex model

Extending the FPRAS for the six-vertex model with an unwindable constraint function beyond two-by-two-intersection-free circuit decompositions and the b≤1/δb\le 1/\deltab≤1/δ regime

Deriving Bethe equations for the XYZ spin chain from the matrix-product-operator construction

Analytic proof of the even-index Yang–Baxter conjectures for descendants of the six-vertex model from the Drinfeld doubles of dihedral group algebras

Completing the approximation-complexity classification of the six-vertex model: the white region of the disordered phase and the Tutte point T(G;3,3)T(G;3,3)T(G;3,3) on planar graphs

Completeness of the homogeneous TTT–QQQ Bethe ansatz for the eight-vertex model with quasi-periodic boundary conditions on an odd number of sites

Completeness of the Wronskian Bethe ansatz for rational gl(m|n) spin chains in arbitrary highest-weight representations and the exceptional specialisation locus

Completing the analytical Bethe ansatz for gl(M|N) super-spin chains: the M=N case, non-commuting boundary matrices, and reflection-superalgebra representations

Bosonic finitized character formulas and the CTM recursion for the one-dimensional sums of the 2×22\times22×2 fused RSOS(m,m′)(m,m')(m,m′) models with m′>2mm'>2mm′>2m

Massive integrable structure of the off-critical logarithmic minimal models LM(p,p';t)

Complete analysis of the open off-critical RSOS quantum chains: integrable boundaries, open-chain spectra, and reality of the non-Hermitian double-row transfer matrices

Full-path-space convergence of multi-type invariant measures and of the ASEP speed process to the stationary horizon

Mixing times and cutoff for the asymmetric simple exclusion process with open boundaries across its three phases (Elboim–Schmid, Conjecture 1.3)

Completing the exact solution of the Ashkin–Teller conformal field theory: the 4-state Potts point, degenerate conformal blocks at rational central charge, and continuation to generic central charge

The SLE(4,g−1,g−1)\mathrm{SLE}(4,\sqrt{g}-1,\sqrt{g}-1)SLE(4,g​−1,g​−1) conjecture for Ashkin–Teller parafermionic interfaces and its Schramm-formula test

Microscopic-to-conformal boundary dictionary of the critical quantum Ashkin–Teller chain: non-universal coupling maps, semi-duality-protected level crossing, and four-state Potts asymptotics

Conformal-field-theory status of transverse-polarized (new) boundary conditions in quantum Potts chains and the transverse-polarized-blob duality beyond the solved endpoints

Open extensions of ballistic macroscopic fluctuation theory for the hard-rod gas: slowly varying external potentials, mesoscopic fluctuating hydrodynamics from inhomogeneous states, and the Toda chain

Theory of finite-size validity of integrable hydrodynamics: why very small Toda chains reproduce thermodynamic ballistic correlation profiles

Multi-sum-to-single-sum transformations: other base summations, an underlying WP-Bailey chain, and combinatorial proofs of the embedded Jacobi-type identities (Mc Laughlin 2016)

Rigorous foundations of Baxter's T−QT-QT−Q relation for the generic periodic XYZ spin chain: the parameter β\betaβ, completeness, singular solutions, and Bethe vectors

Algebraic completion of the Q-operator programme for the XXZ chain at roots of unity: FM-string creation operators, the hidden Onsager-type symmetry, Bethe completeness, and FM-string thermodynamics

Rigorous QQ-system foundation for SO(2r)\mathrm{SO}(2r)SO(2r) spin chains: operator-level proofs for general representations, Wronskian Bethe completeness, and a DrD_rDr​ Baxter TQTQTQ analogue

Polynomiality and commutativity of the Q-operator for the open XXZ spin chain with diagonal boundaries (Vlaar-Weston Conjecture 6.3)

Microscopic verification of the M-theory brane construction of the Kapranov-Voevodsky / Bazhanov-Sergeev / Yoneyama 3D lattice model

Critical behavior, scaling limit, and transfer-matrix spectrum of the N-state Bazhanov-Baxter model on the cubic lattice

Ab initio derivation of generalised hydrodynamics from Bethe wave functions: controlling the sum over permutations in the hydrodynamic limit

Domain of validity of the effective Bethe ansatz for non-integrable spin chains: optimal off-shell states and cost functions, the mechanism of factorized-scattering breakdown, and real-time dynamics

Proof of the Kotousov–Lukyanov conjectures for the scaling-limit norms of Bethe states in the critical XXZ Heisenberg chain

Weak string hypothesis for gl(n|m) supersymmetric spin chains: rigorous foundation

Completing the exact solution of the Izergin-Korepin Gaudin model: Bethe-root structure, eigenstates, and completeness

Physicality of singular Bethe solutions in the remaining open cases: sufficiency for the higher-spin XXZ chain and eigenstate construction for strange repeated-root solutions

Completeness of the Bethe equations for the periodic spin-1/2 XXX Heisenberg chain: proving the counting conjecture

Completeness and soundness of the off-diagonal Bethe ansatz solution of anisotropic spin-1/2 chains with arbitrary boundary fields: the open XYZ chain

Completeness of the coordinate Bethe ansatz for the periodic ASEP with tunable interaction (the general-U Bethe equations of Nakerst–Prosen–Haque)

Low-temperature critical exponents of the Ising model on random trees and locally tree-like random graphs: the susceptibility exponent γ′\gamma'γ′ and the specific-heat exponent α′\alpha'α′

Rigorous organization of Bethe states and effective evaluation of the Bethe variational formula for spin systems on the Bethe lattice

Invisible-state transmutation thresholds for the q = 3 and q = 4 Potts models beyond mean field: planar random graphs and two-dimensional lattices

Phase diagram of semiflexible self-avoiding trails with independent crossing and collision weights on the square lattice

The infinite-dimensional limit of KPZ surface growth and the upper critical dimension of the KPZ universality class

Invariant sets of the period-two splitting map and the complete catalogue of periodic Gibbs measures for the q-state Potts model on the Cayley tree

Classification of weakly periodic Gibbs measures for the two-state hard-core model on Cayley trees: exact multiplicity, extremality, and the (k, i, lambda) phase diagram for normal divisors of index four

Even-length Bethe strings and the antiferromagnetic vacuum of the all-loop su(2) Bethe equations in planar N=4 supersymmetric Yang-Mills theory

Thermodynamic root-density equation for the two-parameter Lieb–Liniger/Cheon–Shigehara interpolation beyond the non-interacting line

Edge-region 2-string deviations, special-object numerics, and counting integers in the excited-state nonlinear integral equations of the spin-1 XXZ chain

Analytic origin and finite-size scaling of the root-organisation rules in the open XXX spin-1/2 chain with non-diagonal boundary fields

Explicit finite-size normalization of nested Bethe ansatz eigenfunctions for continuum multicomponent quantum gases

Rigorous justification of the replica coordinate Bethe ansatz for the log-gamma polymer: Bethe-string norms, completeness, and analytic continuation in replica number

Norms of Bethe states in the Jaynes-Cummings-Gaudin model: the separated-variable integral versus the Gaudin determinant

Prove or refute the Gaudin-type determinant norm formula for Bethe eigenstates of the hard-wall Lieb-Liniger model

Degenerate spectral biorthogonality for string specializations of the q-Hahn coordinate Bethe eigenfunctions

Determinantal and simplified transition-probability formulas for the multi-species ASEP with long-range jumps, and the integrable two-sided long-range extension

Open problems on the spiked spectral boundary of the ASEP: Bethe-root clustering, restricted-cycle random graphs, and Bethe-ansatz completeness

Validity of the string hypothesis for generalized Hubbard models with nonzero Bethe-equation phases

Unphysical singular solutions of the periodic spin-1/2 XXX Bethe equations: classification, thermodynamic-limit abundance, and why string-hypothesis counting still works

Controlled and scalable variance computation for iPEPS ground states and steady states: cell-size and boundary-dimension requirements, long-distance contraction drift, and direct Liouvillian-norm minimization

Finite bond dimension at two-dimensional quantum criticality in iPEPS: Lifshitz-point convergence, operator content of the truncation geometry, and D as a continuum regulator

Exact structure constants of E-series Virasoro minimal models: the polynomiality conjecture, complete q=18q=18q=18 and q=30q=30q=30 formulae, and the unexplained vanishing of C13,13,13evenC^{even}_{13,13,13}C13,13,13even​ in Ep,30E_{p,30}Ep,30​

Completing the R-matrix bootstrap for the 2d O(N) bosonic model with a boundary

Completing the fermionic MLDE classification of two-dimensional fermionic rational conformal field theories and its dictionary to fermionic modular tensor categories

Spinon-type basis and analytic large-k proof of the spinon character formula for graded parafermions (osp^(1,2)k/u^(1)\widehat{\mathfrak{osp}}(1,2)_k/\widehat{\mathfrak{u}}(1)osp​(1,2)k​/u(1))

Free-fermion realisation of the level-h∨h^{\vee}h∨ string functions cρ^ρ^c^{\hat\rho}_{\hat\rho}cρ^​ρ^​​ of sl^(n+1)n+1\widehat{\mathfrak{sl}}(n+1)_{n+1}sl(n+1)n+1​: Han's Conjectures 2.2 and 2.6 at general rank

Quantum integrability of the Coulomb-branch open string: the quantum reflection factor and conserved charges of the D3-brane boundary

Modified boundary crossing for non-invertible symmetries beyond regular module categories: breather spectra, non-regular vacua, and boundary RG flows in 1+1 dimensions

Open problems of the R-matrix bootstrap for the 2d O(N) bosonic model with a boundary

Boundary crossing relations, dressing factors, bound states, and boundary thermodynamics for integrable open spin chains in AdS3/CFT2

Charge-dependent infinite-dimensional reflection matrices in the sine-Gordon model with a boundary: scalar factors, completeness of defect dressing, and classical boundary correspondence

Completing the exact quantum boundary theory of the complex sine-Gordon model on a half line: reflection CDD factors, boundary-pole classification, and boundary-parameter renormalisation

Genuinely integrable boundaries of the 2d O(N) sigma model: closing the mismatch between conformal (M), Lax (U/kappa), and quantum (BYBE) classifications

Tracy-Widom TBA for exact g-functions beyond the self-dual sinh-Gordon point: bound states, internal degrees of freedom, excited states, and the SoV normalization

Completing the boundary scattering theory of massive ϕ1,3\phi_{1,3}ϕ1,3​-perturbed unitary minimal models: the exact ξ\xiξ–(h,λ^)(h,\hat{\lambda})(h,λ^) UV–IR map, reflection matrices for general Cardy superpositions, and boundary residual quantum-group symmetry

Classification of solutions of the boundary Yang-Baxter equation beyond the rational quasi-classical case: trigonometric K-matrices and non-quasi-classical (singular) K-matrices

K-matrices for type-II graded Satake diagrams: the graded and twisted reflection-equation conjectures for quantum super-spherical pairs

Faithfulness of the Bardakov-Bellingeri conjugation representations of surface braid groups on free groups

Open classification of UV completions of integrable TTˉT\bar{T}TTˉ-deformed CFTs: admissible CDD factors, remaining spectra, and UV field content

Rigorous convergence of the two-dimensional unitarity iteration and the continuum fate of the CDD fractal

Analyticity, locality and ultraviolet behaviour of fractional-spin CDD deformations of Zn\mathbb{Z}_nZn​-graded S-matrices

Analytic theory of the corner transfer matrix spectrum and deformed corner Hamiltonian for lattice models on hyperbolic lattices

Direct derivation of the surface–corner scaling function Θs,c(x)\Theta_{s,c}(x)Θs,c​(x) and rigorous proof of the series–CFT identity for the critical Ising rectangle

Completing the corner-operator expansion (COE) of critical profiles near corners: the next nonvanishing apex operators and their amplitudes

Extending the FPRAS for the six-vertex model with an unwindable constraint function beyond two-by-two-intersection-free circuit decompositions and the $b\le 1/\delta$ regime

Completing the approximation-complexity classification of the six-vertex model: the white region of the disordered phase and the Tutte point $T(G;3,3)$ on planar graphs

Completeness of the homogeneous $T$ – $Q$ Bethe ansatz for the eight-vertex model with quasi-periodic boundary conditions on an odd number of sites

Bosonic finitized character formulas and the CTM recursion for the one-dimensional sums of the $2\times2$ fused RSOS $(m,m')$ models with $m'>2m$

The $\mathrm{SLE}(4,\sqrt{g}-1,\sqrt{g}-1)$ conjecture for Ashkin–Teller parafermionic interfaces and its Schramm-formula test

Rigorous foundations of Baxter's $T-Q$ relation for the generic periodic XYZ spin chain: the parameter $\beta$ , completeness, singular solutions, and Bethe vectors

Rigorous QQ-system foundation for $\mathrm{SO}(2r)$ spin chains: operator-level proofs for general representations, Wronskian Bethe completeness, and a $D_r$ Baxter $TQ$ analogue

Low-temperature critical exponents of the Ising model on random trees and locally tree-like random graphs: the susceptibility exponent $\gamma'$ and the specific-heat exponent $\alpha'$

Exact structure constants of E-series Virasoro minimal models: the polynomiality conjecture, complete $q=18$ and $q=30$ formulae, and the unexplained vanishing of $C^{even}_{13,13,13}$ in $E_{p,30}$

Spinon-type basis and analytic large-k proof of the spinon character formula for graded parafermions ( $\widehat{\mathfrak{osp}}(1,2)_k/\widehat{\mathfrak{u}}(1)$ )

Free-fermion realisation of the level- $h^{\vee}$ string functions $c^{\hat\rho}_{\hat\rho}$ of $\widehat{\mathfrak{sl}}(n+1)_{n+1}$ : Han's Conjectures 2.2 and 2.6 at general rank

Completing the boundary scattering theory of massive $\phi_{1,3}$ -perturbed unitary minimal models: the exact $\xi$ – $(h,\hat{\lambda})$ UV–IR map, reflection matrices for general Cardy superpositions, and boundary residual quantum-group symmetry

Open classification of UV completions of integrable $T\bar{T}$ -deformed CFTs: admissible CDD factors, remaining spectra, and UV field content

Analyticity, locality and ultraviolet behaviour of fractional-spin CDD deformations of $\mathbb{Z}_n$ -graded S-matrices

Direct derivation of the surface–corner scaling function $\Theta_{s,c}(x)$ and rigorous proof of the series–CFT identity for the critical Ising rectangle

Free-field resolution and W zero-mode eigenvalue conjectures for $\mathcal{W}[\widehat{g}](p,p')$ minimal models